# Why Is Algebra Important to Know

## Why Is Algebra Important to Know

Algebra is one of the most important subjects you will learn in school. Its applications will not only help you solve equations and word problems in class but also be of great use in daily life.

My dad often said that if you can express your ideas in mathematics, you know what you are talking about. Dad was referring to algebra a part of mathematics that uses letters and other symbols to represent numbers and quantities in formulae and equations.

In this article, I will first give examples of how algebra can be used in the classroom to solve word problems. Next, I will cite different ways of how algebra can be applied to daily life.

## What Is Algebra?

Algebra is a discipline of mathematics that students learn after mastering addition, subtraction, multiplication, division, fractions, and decimals in arithmetic.

I started learning algebra in the ninth grade in 1958. Students today begin learning at an earlier grade. When I was teaching English in a Thailand school in 2012, students were starting to learn algebra in the fifth and sixth grades.

In algebra, letters like x and y and other symbols are used to represent numbers and quantities in formulae and equations.

## Invention of Algebra

According to the website Aljazeera, Muhammed ibn Musa Al-Khwarizmi, a ninth-century Muslim mathematician and astronomer, is the father of algebra. The word algebra is derived from the title of his book, *Kitab al-Jabr*.

## Importance of Algebra

Basic algebraic principles are applied in other math courses such as geometry, trigonometry, and calculus. Also, algebra can be used to solve practical word problems in all other math problems using formulae and equations.

## Applying Algebra to Solve Word Problems in the Classroom

Here are two examples of how algebra can be used to solve word problems.

1. Age Problems

Let's say we have a word problem stated like this. There are two persons, Peter and Paul. Peter is older than Paul. The sum of their ages is 30 and the difference is 6. How old are Peter and Paul?

In solving a word problem, the first step is to ask what information is being sought. Clearly, the question wants to know the ages of Peter and Paul. We know that Peter is older than Paul.

Using algebra, we use x to represent the age of Peter and use y to represent the age of Paul. The sum of their ages is 30 can be represented using x + y = 30. The difference of their ages is 6 can be represented with the equation x - y = 6.

We then solve the two equations by adding them to find the values of x and y.

x + y = 30

x - y = 6

2x = 36

x = 18

We find that x or Peter is 18. By substituting 18 for x in the equation x + y = 30,

18 + y = 30, we solve and find that y = 12. Paul is thus 12.

We check our answers by substituting the ages of Peter and Paul in the equations.

18 + 12 = 30

18 - 12 = 6

2. Trigonometry Problem

Let's now look at this problem. Assume that we have a right triangle in which the base is 4 and the height 3. The problem is to determine the length of the hypotenuse.

In solving this problem, we must understand the Pythagorean Theorem which states that the sum of the base squared and height squared equals the hypotenuse squared.

If the base is represented by a, the height by b, and the hypotenuse by c, we can express the Pythagorean Theorem as a2 + b2 = c2.

In solving for the length of the hypotenuse or c, we substitute the known values of the base and height into the equation as

4 squared + 3 squared = c2

In solving this equation we get

16 + 9 = c2

25 = c2

By taking the square root of both sides of the equation, we get

5 = c in which c is the length of the hypotenuse.

## Applying Algebra to Daily Life

Many countries of the world express temperature in degrees Celsius unlike degrees Fahrenheit used in the United States.

if the temperature is, for example, 30 degrees Celsius in Thailand, what is this equivalent to in Fahrenheit degrees?

To solve this problem, we must know that degrees Fahrenheit equals 1.8 times degrees Celsius plus 32 degrees. This is expressed in equation form as

F degrees = 1.8 x C degrees + 32 degrees

Substituting 30 degrees Celsius into this equation we get

F degrees = 1.8 x 30 degrees + 32 degrees or

F degrees = 54 degrees + 32 degrees

F degrees = 86 degrees

Hence we have determined that 30 degrees Celsius equals 86 degrees Fahrenheit.

Another application of algebra to daily life is in using equivalent ratios. I encountered the following problem when giving a test as a teacher in Thailand. The test which I had composed had 60 questions on it. If a student, for example, had 22 questions correct, what was his percentage score?

In solving this problem, we must understand that percentages are based on 100. We can set up equivalent ratios to solve this problem as follows

x/100 = 22/60 where x is the score based on percentage points

By cross multiplying in solving this equation we get

x(60) = 22(100)

60x = 2200 By dividing both sides of the equation by 60, we arrive at

x = 36.6 or 37 percent as the score on the test.

These are only two examples showing how algebra can be applied to daily life. People will encounter many more in their lives. Algebra is important to know in life.

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

**© 2019 Paul Richard Kuehn**

## Comments

Hi.

You have covered some important areas of mathematics involving algebraic manipulation. Some suggestions:

Pythagoras' theorem is not really part of trigonometry because only side lengths of a triangle are used, not angles. Hence it might be better to use THEOREM OF PYTHAGORAS.

A diagram illustrating Pythagoras' Theorem might be useful.

Show powers of 2 as raised numbers or as, for example, a^2+b^2=c^2

After x/100=22/60 you can multiply by 100 to get x=100*22/60

Regards

George

I was one of the few girls in school that liked algebra. I found myself using algebraic formulas working in the ICU as a RN. So often children don't think they need to learn various subjets, but this is an important cass. I think this is a very good article.

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